As Sddsddean points out, it would be a great deal easier to answer your question if we knew where you were starting from! It's probably not much use us finding flights out of, say, Southampton if you live near Aberdeen;-)
The following operators have scheduled services to Madeira:
Flyglobespan (from Edinburgh)
easyJet (from Bristol, Gatwick & Stansted)
TAP-Portugal (from Gatwick & Heathrow))
Scheduled services normally operate daily (or at least several days per week).
The following operators have charter flights to Madeira. Charter flights are normally intended primarily for passengers booking package holidays. (So they only operate on those days when the package holidays start and finish). Not all operators make seats available on a 'flight only' basis; those that do might only make such seats available fairly close to the departure date:
Thomson Airways (from Birmingham, Bristol, Cardiff, Gatwick & Manchester)
Thomas Cook (from Glasgow, Gatwick & Manchester)
Palmair (from Bournemouth, using aircraft & crew provided by Jet2).
Chris